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Unformatted text preview: Assignment 5 – ACTSC 433/833, Winter 2012 (Due at the beginning of the class on March 29) For this assignment, if needed, you can use any software such as Maple, Mathe- matica, and MATLAB to find roots of an equation. 1. A one-covariate Cox proportional hazards model of h ( x ) = h ( x ) e βZ is used to study losses from two lines of business. Line 1 has Z = 0 and line 2 has Z = 1. A sample of size five is taken from each line. Line 1 : 135 , 160 , 240 , 320 , 380 . Line 2 : 115 , 140 , 205 , 245 , 285 . The baseline survival function is S ( x ) = 100 x α , x > 100 , α > 0. (a) Determine the maximum likelihood estimates of α and β . [10 marks] (b) Determine the maximum likelihood estimate for the median loss in line 1. [4 marks] (c) Determine the maximum likelihood estimate for the mean loss in line 2. [4 marks] (d) Determine the maximum likelihood estimate for the probability that a loss in line 2 will exceed 200. [2 marks] 2. Repeat Question 1 using a different baseline survival function, namely, assume that a2....
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- Winter '09
- Maximum likelihood, class a, maximum likelihood estimate, Survival analysis